# Bounded Coupled AI Learning Dynamics in Tri-Hierarchical Drone Swarms

arXiv: https://arxiv.org/abs/2603.20333 · HTML: https://mlsanity.com/paper/2603.20333/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 25 references that are in the map.
- First posted on arXiv 20 Mar 2026.

## Builds on (most cited first, 13 of 13)

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- [The Surprising Effectiveness of PPO in Cooperative, Multi-Agent Games](https://mlsanity.com/paper/2103.01955/) (2021)
- [Multi-Agent Reinforcement Learning: A Selective Overview of Theories and Algorithms](https://mlsanity.com/paper/1911.10635/) (2019)
- [Monotonic Value Function Factorisation for Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2003.08839/) (2020)
- [On the Convergence Theory of Gradient-Based Model-Agnostic Meta-Learning Algorithms](https://mlsanity.com/paper/1908.10400/) (2019)
- [Continuous Adaptation via Meta-Learning in Nonstationary and Competitive Environments](https://mlsanity.com/paper/1710.03641/) (2017)
- [A Survey of Learning in Multiagent Environments: Dealing with Non-Stationarity](https://mlsanity.com/paper/1707.09183/) (2017)
- [Differentiable plasticity: training plastic neural networks with backpropagation](https://mlsanity.com/paper/1804.02464/) (2018)
- [Meta-Learning through Hebbian Plasticity in Random Networks](https://mlsanity.com/paper/2007.02686/) (2020)
- [Theoretical Convergence of Multi-Step Model-Agnostic Meta-Learning](https://mlsanity.com/paper/2002.07836/) (2020)
- [Evolving and Merging Hebbian Learning Rules: Increasing Generalization by Decreasing the Number of Rules](https://mlsanity.com/paper/2104.07959/) (2021)

## Abstract (arXiv)

Modern autonomous multi-agent systems combine heterogeneous learning mechanisms operating at different timescales. An open question remains: can one formally guarantee that coupled dynamics of such mechanisms stay within the admissible operational regime? This paper studies a tri-hierarchical swarm learning system where three mechanisms act simultaneously: (1) local Hebbian online learning at individual agent level (fast timescale, 10-100 ms); (2) multi-agent reinforcement learning (MARL) for tactical group coordination (medium timescale, 1-10 s); (3) meta-learning (MAML) for strategic adaptation (slow timescale, 10-100 s). Four results are established. The Bounded Total Error Theorem shows that under contractual constraints on learning rates, Lipschitz continuity of inter-level mappings, and weight stabilization, total suboptimality admits a component-wise upper bound uniform in time. The Bounded Representation Drift Theorem gives a worst-case estimate of how Hebbian updates affect coordination-level embeddings during one MARL cycle. The Meta-Level Compatibility Theorem provides sufficient conditions under which strategic adaptation preserves lower-level invariants. The Non-Accumulation Theorem proves that error does not grow unboundedly over time.